Parallax Tracking

Multi-target tracking, sensor fusion, and estimation — shown working, and measured.

Below: two drones track six targets with nothing but bearing measurements — a camera measures an angle, not a distance. One viewpoint cannot localise anything; the geometry between viewpoints is what does. Drag a drone and watch the uncertainty ellipses reshape.

Everything runs in your browser on synthetic data, from a cold start — nothing is precomputed or replayed. Algorithms from the published literature: global nearest neighbour, multiple-hypothesis tracking, S-D assignment.

Parallax Trackingבס״ד

Multi-target tracking, sensor fusion and estimation

Interactive tutorial · with Claude AI assistance

Parallax Tracking — every figure below is computed as you read it

Table IResult at the current epoch
Live: the running scenario's own numbers, not a recorded benchmark. For reproducible medians see Table III.
Fig. 2aMean 2σ major axis, recent history
Step changes are sensors being added or removed; the sawtooth is track birth and death.
Table IIIThe four algorithms, five-seed medians
Method2 sen.3 sen.4 sen. ms/stepvalidation
OSPA at cutoff 200 m and clutter 2, in metres; lower is better. Every cell is the median of five seeds — the same configuration has been measured spanning 4.5 to 162.9 across seeds, so a single-seed figure is noise. Tuned on one seed set, reported on a disjoint one. Timing measured solo at three sensors. Click a row to open that article.
Fig. 2. The Cramér–Rao position bound as a body. One target at the origin, its sensors around it, and the 2σ covariance ellipsoids of a converged EKF and of a batch Gauss–Newton solution, both normalised by σ · reff so the absolute noise level cancels. Drag to orbit; the sensor list and both estimators are behind the gear. Three-dimensional because with a single target there is nothing to associate, hence no filter and nothing that can diverge.
Table IIGeometry and accuracy for the constellation above

Appendix — common to all four methods

References

  1. D. B. Reid, “An algorithm for tracking multiple targets,” IEEE Trans. Autom. Control, vol. 24, no. 6, pp. 843–854, 1979.
  2. Y. Bar-Shalom and E. Tse, “Tracking in a cluttered environment with probabilistic data association,” Automatica, vol. 11, no. 5, pp. 451–460, 1975.
  3. K. G. Murty, “An algorithm for ranking all the assignments in order of increasing cost,” Oper. Res., vol. 16, no. 3, pp. 682–687, 1968.
  4. S. Deb, M. Yeddanapudi, K. Pattipati and Y. Bar-Shalom, “A generalized S-D assignment algorithm for multisensor-multitarget state estimation,” IEEE Trans. Aerosp. Electron. Syst., vol. 33, no. 2, pp. 523–538, 1997.
  5. D. Schuhmacher, B.-T. Vo and B.-N. Vo, “A consistent metric for performance evaluation of multi-object filters,” IEEE Trans. Signal Process., vol. 56, no. 8, pp. 3447–3457, 2008.
  6. S. C. Nardone and V. J. Aidala, “Observability criteria for bearings-only target motion analysis,” IEEE Trans. Aerosp. Electron. Syst., vol. 17, no. 2, pp. 162–166, 1981.
  7. D. P. Bertsekas, “The auction algorithm: a distributed relaxation method for the assignment problem,” Ann. Oper. Res., vol. 14, pp. 105–123, 1988.
  8. R. B. Langley, “Dilution of precision,” GPS World, vol. 10, no. 5, pp. 52–59, 1999.
  9. Y. Bar-Shalom, S. S. Blackman and R. J. Fitzgerald, “Dimensionless score function for multiple hypothesis tracking,” IEEE Trans. Aerosp. Electron. Syst., vol. 43, no. 1, pp. 392–400, 2007.
  10. A. Wald, “Sequential tests of statistical hypotheses,” Ann. Math. Statist., vol. 16, no. 2, pp. 117–186, 1945.
  11. J. Munkres, “Algorithms for the assignment and transportation problems,” J. SIAM, vol. 5, no. 1, pp. 32–38, 1957.
  12. P. R. J. Östergård, “A new algorithm for the maximum-weight clique problem,” Nordic J. Computing, vol. 8, no. 4, pp. 424–436, 2001.
  13. T. A. Feo, M. G. C. Resende and S. H. Smith, “A greedy randomized adaptive search procedure for maximum independent set,” Oper. Res., vol. 42, no. 5, pp. 860–878, 1994.
  14. T. Kurien, “Issues in the design of practical multitarget tracking algorithms,” in Multitarget-Multisensor Tracking: Advanced Applications, Y. Bar-Shalom, Ed. Artech House, 1990, ch. 3.

What to look for

Use the three preset buttons. With two viewpoints and clutter, the tracker can confirm a ghost — a track at a crossing of bearings that belongs to no real target — and hold it with full confidence, because two static bearing-only sensors genuinely cannot tell some ghost worlds from the true one. A third viewpoint breaks the symmetry and the ghost dissolves. Fusing several scans per sensor before deciding (multi-frame assignment) makes tracking near-perfect.

That is the parallax lesson: performance lives in the geometry and in how long you wait before committing to a decision, not in any single tuning knob.

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